Finite Group Databasebeta

← #29576754

Subgroups — #29576754

Order 15616.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456744C211yesmaximal, characteristic
2#21446651C211yesmaximal, characteristic
3#21444500C211yesmaximal, characteristic, complemented
4#21444378C211yesmaximal, characteristic
5#21443677C211yesmaximal, characteristic, complemented
6#21443648C211yesmaximal, characteristic, complemented
7C61×#2331C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840136C412yescomplemented
10#16840112C412yescomplemented
11#16839964—22no—
12#16839901—22no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15#16839786C2211yescharacteristic
16C2×#14519705—21no—
17C2×#14519705—21no—
18#16839511—22no—
19#16839495—22no—
20C2×C4⋊Q8×C61C2211yescharacteristic
21C61×#391—22no—
22C61×#389—21no—
23C61×#387—22no—
24C61×#382C2211yescharacteristic
25C4×C4⋊C4×C61—21no—
26C61×#376C2211yescharacteristic
27C2×#11758222—21no—
28C2×#11758201—24no—
29C2×#11758194—21no—
30#14519777C2×C411yescharacteristic
31#14519774C2×C411yescharacteristic
32#14519765—21no—
33#14519751—21no—
34#14519751—21no—
35C4×D244—21no—
36C4×D244—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41#14519705—42no—
42#14519705—42no—
43#14519701—24no—
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46C4×#92418—21no—
47C4×#92418C2×C412yes—
48C22×Q8×C61D412yes—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61C2×C412yes—
52C4⋊Q8×C61D412yes—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—22no—
57C2×C42×C61—22no—
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#95×C61—22no—
62#95×C61—22no—
63#95×C61—21no—
64#95×C61—21no—
65#95×C61—21no—
66#95×C61D412yes—
67C2×Q8×C61—22no—
68C2×Q8×C61—82no—
69C2×Q8×C61C22⋊C414yes—
70C22×C4×C61—21no—
71C22×C4×C61—22no—
72C22×C4×C61—21no—
73C22×C4×C61—22no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—41no—
78#11758222—41no—
79#11758222—41no—
80#11758222—41no—
81#11758222—41no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×C4×D61—41no—
86C2×Dic122—21no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—82no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—82no—
98C42×C61SD1612yescomplemented
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103#11758201—84no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—22no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114C22×D61—41no—
115Q8×C61—44no—
116Q8×C61—82no—
117C2×C4×C61—24no—
118C2×C4×C61—22no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×C4×C61C2×SD1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C22⋊D61—81no—
142C22⋊D61—81no—
143C2×Dic61—41no—
144D244—42no—
145D244—41no—
146D244—41no—
147D244—81no—
148C4×D61—81no—
149C4×D61—81no—
150Dic122—41no—
151Dic122—41no—
152#92418—42no—
153#92418—81no—
154#92418—81no—
155#9301—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61#38611yescharacteristic
159C22×C61#44811yescharacteristic
160C22×C61#44911yescharacteristic
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—81no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—42no—
169C4×C61—44no—
170C4×C61—82no—
171C4×C61—81no—
172C4×C61C4×SD1611yescharacteristic
173C4×C61#44011yescharacteristic
174C4×C61#46011yescharacteristic
175C4×C61#46411yescharacteristic
176Dic61—81no—
177#3206—611no—
178#2331D6111yescharacteristic, complemented
179#1963—611no—
180#1548—611no—
181#1517—611no—
182#1286—611no—
183#1274—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#188011yescharacteristic
187C2×C61#190511yescharacteristic
188C2×C61#191111yescharacteristic
189D61—161no—
190#532—611no—
191C2×C4⋊Q8C2×D6111yescharacteristic
192#492—612no—
193#487—612no—
194#461—1222no—
195#448—1222no—
196#431—611no—
197#431—611no—
198#423—611no—
199C2×#104—1221no—
200C2×#104—1221no—
201#391—22no—
202#389—21no—
203#387—22no—
204#382C2×D6111yescharacteristic
205C4×C4⋊C4—21no—
206#376C2×D6111yescharacteristic
207#333—1222no—
208#327—1222no—
209C61#930111yescharacteristic, complemented, Sylow
210C2×#41—1221no—
211C22×Q8C22⋊D6112yes—
212C2×SD16—1224no—
213C2×M16—1221no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—611no—
217C4⋊Q8C4×D6112yes—
218C4⋊Q8D24412yes—
219#127—611no—
220#124—1221no—
221#121—1221no—
222#121—1221no—
223C4×D4—1221no—
224C4×D4—1221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C42—22no—
230C2×C42C22⋊D6111yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22×D6111yescharacteristic
233C4⋊C8—1221no—
234C4⋊C8—1221no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237#104—2442no—
238#104—2442no—
239#103—1224no—
240C22⋊C8—1221no—
241C22⋊C8—1221no—
242C4×C8—612no—
243C4×C8—1221no—
244#95—22no—
245#95—22no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95C22⋊D6112yes—
250#41—2441no—
251#41—2441no—
252#41—2441no—
253#41—2441no—
254C2×Q8—22no—
255C2×Q8—82no—
256C2×Q8—1221no—
257C2×Q8#1175819814yes—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—2441no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—2441no—
267C22×C4C2×C22⋊D6111yescharacteristic
268C22×C4C2×C22⋊D6111yescharacteristic
269C22×C4C2×C22⋊D6111yescharacteristic
270SD16—4884no—
271M16—2441no—
272M16—2441no—
273C2×C8—1222no—
274C2×C8—2441no—
275C2×C8—2441no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—82no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—82no—
291C42#1175820112yescomplemented
292C42C2×C4×D6111yescharacteristic
293C42C2×D24411yescharacteristic
294C42#1175822211yescharacteristic
295C42#1175822211yescharacteristic
296C23—2441no—
297C23#1451974611yescharacteristic
298Q8—44no—
299Q8—82no—
300Q8—2441no—
301Q8—2441no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305D4—2442no—
306D4—2441no—
307D4—2441no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—2441no—
325C2×C4C2×#1175819811yescharacteristic
326C2×C4C4×C22⋊D6111yescharacteristic
327C2×C4C4×C22⋊D6111yescharacteristic
328C2×C4#1451975111yescharacteristic
329C2×C4#1451975111yescharacteristic
330C2×C4#1451976011yescharacteristic
331C2×C4C2×#1175820111yescharacteristic
332C2×C4#1451979711yescharacteristic
333C2×C4#1451980211yescharacteristic
334C2×C4#1451980811yescharacteristic
335C8—4881no—
336C8—4881no—
337C8—2442no—
338C22—21no—
339C22—21no—
340C22—4881no—
341C22—4881no—
342C22—4881no—
343C22#1683964111yescharacteristic
344C22#1683990111yescharacteristic
345C22#1683990711yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C4—4881no—
355C4C4×#1175820111yescharacteristic
356C4#1683986011yescharacteristic
357C4#1683996211yescharacteristic
358C4#1683998411yescharacteristic
359C2—21no—
360C2—21no—
361C2—9761no—
362C2#2144617411yescharacteristic
363C2#2144631311yescharacteristic
364C2#2144635111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2331C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#2331D61
hypocenterC61#9301
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2331

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21444500C2semidirect
5. #21443677C2semidirect
6. #21443648C2semidirect
7. C61×#2331C2semidirect
9. #16840136C4semidirect
10. #16840112C4semidirect
98. C42×C61SD16semidirect
178. #2331D61semidirect
209. C61#9301semidirect
291. C42#11758201semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214567442
#214466512
#214445002
#214443782
#214436772
#214436482
C61×#23312
#930161